In [2]:
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import warnings
warnings.filterwarnings("ignore")
In [3]:
import matplotlib.pyplot as plt
import seaborn as sns
from sklearn.manifold import TSNE
from sklearn import preprocessing
from sklearn.preprocessing import MinMaxScaler
from sklearn.cluster import KMeans
from sklearn.decomposition import PCA, KernelPCA
from sklearn.cluster import DBSCAN
# just to get multuple output from the same cell.
from IPython.core.interactiveshell import InteractiveShell
InteractiveShell.ast_node_interactivity = "all"
In [92]:
def Bar(df,Column_name,bins):
"""Plot a menengful bar plot.
Args:
df (Pandas Dataframe): DataFrame with all the records.
Column_name (string): the name of the column we wont to plot.
bins (list): Deviding our bar plot acording to those bins.
"""
plt.figure(figsize=(18,7))
freq, bins, p = plt.hist(df[Column_name], bins=bins,rwidth=0.9)
# x coordinate for labels
bin_centers = np.diff(bins)*0.5 + bins[:-1]
n = 0
for fr, x, patch in zip(freq, bin_centers,p):
height = int(freq[n])
plt.annotate("{}%".format(round(height*100 / df.shape[0],2)),
xy = (x, height),
xytext = (0,0.2),
textcoords = "offset points",
ha = 'center', va = 'bottom'
)
n = n+1
plt.grid()
plt.xticks(bins)
plt.title(Column_name)
plt.show;
1. Read the dataset¶
First dowmload the data set from this link https://www.kaggle.com/code/sadkoktaybicici/credit-card-data-clustering-k-mean/data then import it in python.
In [5]:
#read the data
data_path = 'D:\Study\ITI\Machine Learning 2\PCA\CC GENERAL.csv' #the path where you downloaded the data
df = pd.read_csv(data_path)
print('The shape of the dataset is:', df.shape)
The shape of the dataset is: (8950, 18)
In [5]:
df.head()
Out[5]:
| CUST_ID | BALANCE | BALANCE_FREQUENCY | PURCHASES | ONEOFF_PURCHASES | INSTALLMENTS_PURCHASES | CASH_ADVANCE | PURCHASES_FREQUENCY | ONEOFF_PURCHASES_FREQUENCY | PURCHASES_INSTALLMENTS_FREQUENCY | CASH_ADVANCE_FREQUENCY | CASH_ADVANCE_TRX | PURCHASES_TRX | CREDIT_LIMIT | PAYMENTS | MINIMUM_PAYMENTS | PRC_FULL_PAYMENT | TENURE | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | C10001 | 40.900749 | 0.818182 | 95.40 | 0.00 | 95.4 | 0.000000 | 0.166667 | 0.000000 | 0.083333 | 0.000000 | 0 | 2 | 1000.0 | 201.802084 | 139.509787 | 0.000000 | 12 |
| 1 | C10002 | 3202.467416 | 0.909091 | 0.00 | 0.00 | 0.0 | 6442.945483 | 0.000000 | 0.000000 | 0.000000 | 0.250000 | 4 | 0 | 7000.0 | 4103.032597 | 1072.340217 | 0.222222 | 12 |
| 2 | C10003 | 2495.148862 | 1.000000 | 773.17 | 773.17 | 0.0 | 0.000000 | 1.000000 | 1.000000 | 0.000000 | 0.000000 | 0 | 12 | 7500.0 | 622.066742 | 627.284787 | 0.000000 | 12 |
| 3 | C10004 | 1666.670542 | 0.636364 | 1499.00 | 1499.00 | 0.0 | 205.788017 | 0.083333 | 0.083333 | 0.000000 | 0.083333 | 1 | 1 | 7500.0 | 0.000000 | NaN | 0.000000 | 12 |
| 4 | C10005 | 817.714335 | 1.000000 | 16.00 | 16.00 | 0.0 | 0.000000 | 0.083333 | 0.083333 | 0.000000 | 0.000000 | 0 | 1 | 1200.0 | 678.334763 | 244.791237 | 0.000000 | 12 |
2. Data investigation¶
in this part you need to check the data quality and assess any issues in the data as:
- null values in each column
- each column has the proper data type
- outliers
- duplicate rows
- distribution for each column (skewness)
comment each issue you find
In [6]:
# Let's see the data types and non-null values for each column
df.info()
<class 'pandas.core.frame.DataFrame'> RangeIndex: 8950 entries, 0 to 8949 Data columns (total 18 columns): # Column Non-Null Count Dtype --- ------ -------------- ----- 0 CUST_ID 8950 non-null object 1 BALANCE 8950 non-null float64 2 BALANCE_FREQUENCY 8950 non-null float64 3 PURCHASES 8950 non-null float64 4 ONEOFF_PURCHASES 8950 non-null float64 5 INSTALLMENTS_PURCHASES 8950 non-null float64 6 CASH_ADVANCE 8950 non-null float64 7 PURCHASES_FREQUENCY 8950 non-null float64 8 ONEOFF_PURCHASES_FREQUENCY 8950 non-null float64 9 PURCHASES_INSTALLMENTS_FREQUENCY 8950 non-null float64 10 CASH_ADVANCE_FREQUENCY 8950 non-null float64 11 CASH_ADVANCE_TRX 8950 non-null int64 12 PURCHASES_TRX 8950 non-null int64 13 CREDIT_LIMIT 8949 non-null float64 14 PAYMENTS 8950 non-null float64 15 MINIMUM_PAYMENTS 8637 non-null float64 16 PRC_FULL_PAYMENT 8950 non-null float64 17 TENURE 8950 non-null int64 dtypes: float64(14), int64(3), object(1) memory usage: 1.2+ MB
Single null value at CREDIT_LIMIT, and 313 null values at MINIMUM_PAYMENTS.
each column has the proper data type exept for CUST_ID which has no menneing so will be droped.
In [7]:
round(df.isnull().sum(axis=0)*100/df.shape[0],2)
Out[7]:
CUST_ID 0.00 BALANCE 0.00 BALANCE_FREQUENCY 0.00 PURCHASES 0.00 ONEOFF_PURCHASES 0.00 INSTALLMENTS_PURCHASES 0.00 CASH_ADVANCE 0.00 PURCHASES_FREQUENCY 0.00 ONEOFF_PURCHASES_FREQUENCY 0.00 PURCHASES_INSTALLMENTS_FREQUENCY 0.00 CASH_ADVANCE_FREQUENCY 0.00 CASH_ADVANCE_TRX 0.00 PURCHASES_TRX 0.00 CREDIT_LIMIT 0.01 PAYMENTS 0.00 MINIMUM_PAYMENTS 3.50 PRC_FULL_PAYMENT 0.00 TENURE 0.00 dtype: float64
Since the null values are only 3.5% of the data, we can drob them.
In [ ]:
# This will print basic statistics for numerical columns
df.describe().T
Out[Â ]:
| count | mean | std | min | 25% | 50% | 75% | max | |
|---|---|---|---|---|---|---|---|---|
| BALANCE | 8636.0 | 1601.224893 | 2095.571300 | 0.000000 | 148.095189 | 916.855459 | 2105.195853 | 19043.13856 |
| BALANCE_FREQUENCY | 8636.0 | 0.895035 | 0.207697 | 0.000000 | 0.909091 | 1.000000 | 1.000000 | 1.00000 |
| PURCHASES | 8636.0 | 1025.433874 | 2167.107984 | 0.000000 | 43.367500 | 375.405000 | 1145.980000 | 49039.57000 |
| ONEOFF_PURCHASES | 8636.0 | 604.901438 | 1684.307803 | 0.000000 | 0.000000 | 44.995000 | 599.100000 | 40761.25000 |
| INSTALLMENTS_PURCHASES | 8636.0 | 420.843533 | 917.245182 | 0.000000 | 0.000000 | 94.785000 | 484.147500 | 22500.00000 |
| CASH_ADVANCE | 8636.0 | 994.175523 | 2121.458303 | 0.000000 | 0.000000 | 0.000000 | 1132.385490 | 47137.21176 |
| PURCHASES_FREQUENCY | 8636.0 | 0.496000 | 0.401273 | 0.000000 | 0.083333 | 0.500000 | 0.916667 | 1.00000 |
| ONEOFF_PURCHASES_FREQUENCY | 8636.0 | 0.205909 | 0.300054 | 0.000000 | 0.000000 | 0.083333 | 0.333333 | 1.00000 |
| PURCHASES_INSTALLMENTS_FREQUENCY | 8636.0 | 0.368820 | 0.398093 | 0.000000 | 0.000000 | 0.166667 | 0.750000 | 1.00000 |
| CASH_ADVANCE_FREQUENCY | 8636.0 | 0.137604 | 0.201791 | 0.000000 | 0.000000 | 0.000000 | 0.250000 | 1.50000 |
| CASH_ADVANCE_TRX | 8636.0 | 3.313918 | 6.912506 | 0.000000 | 0.000000 | 0.000000 | 4.000000 | 123.00000 |
| PURCHASES_TRX | 8636.0 | 15.033233 | 25.180468 | 0.000000 | 1.000000 | 7.000000 | 18.000000 | 358.00000 |
| CREDIT_LIMIT | 8636.0 | 4522.091030 | 3659.240379 | 50.000000 | 1600.000000 | 3000.000000 | 6500.000000 | 30000.00000 |
| PAYMENTS | 8636.0 | 1784.478099 | 2909.810090 | 0.049513 | 418.559237 | 896.675701 | 1951.142090 | 50721.48336 |
| MINIMUM_PAYMENTS | 8636.0 | 864.304943 | 2372.566350 | 0.019163 | 169.163545 | 312.452292 | 825.496463 | 76406.20752 |
| PRC_FULL_PAYMENT | 8636.0 | 0.159304 | 0.296271 | 0.000000 | 0.000000 | 0.000000 | 0.166667 | 1.00000 |
| TENURE | 8636.0 | 11.534391 | 1.310984 | 6.000000 | 12.000000 | 12.000000 | 12.000000 | 12.00000 |
In [ ]:
df.duplicated().sum()
Out[Â ]:
0
No duplicated rows.
In [ ]:
correlation_matrix = df.corr()
plt.figure(figsize=(10, 8))
sns.heatmap(correlation_matrix, annot=True, cmap='coolwarm', fmt=".2f", linewidths=0.5)
plt.title('Correlation Matrix')
plt.show()
Many features are highly correlated like :
PURCHASES and ONEOFF_PURCHASES
PURCHASES and INSTALLMENTS_PURCHASES
CASH_ADVANCE_FREQUENCY and CASH_ADVANCE_TRX
and so on.... The similarity in their names suggests they are calculated ( depends ) on one another.
In [10]:
noID = df.drop(columns="CUST_ID")
sns.pairplot(noID)
Out[10]:
<seaborn.axisgrid.PairGrid at 0x1121afe95d0>
Here we can see some pattern between some features, some are positively correlated, some are negatively correlated and some almost have no crolation.
In [11]:
for X in noID.columns:
sns.boxplot(x=df[X])
plt.show()
Out[11]:
<Axes: xlabel='BALANCE'>
Out[11]:
<Axes: xlabel='BALANCE_FREQUENCY'>
Out[11]:
<Axes: xlabel='PURCHASES'>
Out[11]:
<Axes: xlabel='ONEOFF_PURCHASES'>
Out[11]:
<Axes: xlabel='INSTALLMENTS_PURCHASES'>
Out[11]:
<Axes: xlabel='CASH_ADVANCE'>
Out[11]:
<Axes: xlabel='PURCHASES_FREQUENCY'>
Out[11]:
<Axes: xlabel='ONEOFF_PURCHASES_FREQUENCY'>
Out[11]:
<Axes: xlabel='PURCHASES_INSTALLMENTS_FREQUENCY'>
Out[11]:
<Axes: xlabel='CASH_ADVANCE_FREQUENCY'>
Out[11]:
<Axes: xlabel='CASH_ADVANCE_TRX'>
Out[11]:
<Axes: xlabel='PURCHASES_TRX'>
Out[11]:
<Axes: xlabel='CREDIT_LIMIT'>
Out[11]:
<Axes: xlabel='PAYMENTS'>
Out[11]:
<Axes: xlabel='MINIMUM_PAYMENTS'>
Out[11]:
<Axes: xlabel='PRC_FULL_PAYMENT'>
Out[11]:
<Axes: xlabel='TENURE'>
almost all feuters are highly skewed.
CASH_ADVANCE_FREQUENCY : A score (between 0 and 1) indicating how often cash advances are taken using the card.
Some values are more than one I think we should applay thrathhold or drop them.
In [ ]:
(df == 0).mean(axis=0)*100
Out[Â ]:
CUST_ID 0.000000 BALANCE 0.893855 BALANCE_FREQUENCY 0.893855 PURCHASES 22.837989 ONEOFF_PURCHASES 48.067039 INSTALLMENTS_PURCHASES 43.754190 CASH_ADVANCE 51.709497 PURCHASES_FREQUENCY 22.826816 ONEOFF_PURCHASES_FREQUENCY 48.067039 PURCHASES_INSTALLMENTS_FREQUENCY 43.743017 CASH_ADVANCE_FREQUENCY 51.709497 CASH_ADVANCE_TRX 51.709497 PURCHASES_TRX 22.837989 CREDIT_LIMIT 0.000000 PAYMENTS 2.681564 MINIMUM_PAYMENTS 0.000000 PRC_FULL_PAYMENT 65.955307 TENURE 0.000000 dtype: float64
So many sparce features.
In [ ]:
df.columns
Out[Â ]:
Index(['CUST_ID', 'BALANCE', 'BALANCE_FREQUENCY', 'PURCHASES',
'ONEOFF_PURCHASES', 'INSTALLMENTS_PURCHASES', 'CASH_ADVANCE',
'PURCHASES_FREQUENCY', 'ONEOFF_PURCHASES_FREQUENCY',
'PURCHASES_INSTALLMENTS_FREQUENCY', 'CASH_ADVANCE_FREQUENCY',
'CASH_ADVANCE_TRX', 'PURCHASES_TRX', 'CREDIT_LIMIT', 'PAYMENTS',
'MINIMUM_PAYMENTS', 'PRC_FULL_PAYMENT', 'TENURE'],
dtype='object')
In [ ]:
Bar(df,"BALANCE",[0,500,1000,2000,5000,10000,20000])
More than 90% have less than 5K in their credit card balance.
In [54]:
Bar(df,"MINIMUM_PAYMENTS",[0,500,1000,2000,5000,10000,20000])
MINIMUM_PAYMENTS ===> The minimum amount required to be paid each billing cycle to avoid late fees.
Also more than 90% have less than 5K in minimum payments.
This make sense because most data is left skewed.
In [ ]:
Bar(df,"PURCHASES",[0,500,1000,2000,5000,10000,20000])
In [ ]:
Bar(df,"PURCHASES_FREQUENCY",[0,0.1,0.3,0.6,0.9,1])
PURCHASES_FREQUENCY is a score indicating how frequently purchases are made using the card.
Looks like a 30% of the users are inactive (rarely using the card ).
In [9]:
Bar(df,"CREDIT_LIMIT",[0,1000,2500,10000,20000,30000])
Almost 90% have credit limit bellow 10K
In [23]:
Bar(df,"CASH_ADVANCE",[0,1000,2500,10000,20000,30000])
data is Highly consentrated bellow 3K.
In [ ]:
Bar(df,"TENURE",[6,7,8,9,10,11,12])
df["TENURE"].value_counts()
Out[Â ]:
12 7584 11 365 10 236 6 204 8 196 7 190 9 175 Name: TENURE, dtype: int64
TENURE ====> The length of time (in months) the customer has keept the credit card account.
Almost all the users keept the card for 12 monthes or maybe more.
Reducing the number of dimensions down to two (or three) makes it possible to plot a high-dimensional training set on a graph and
often gain some important insights by visually detecting patterns, such as clusters.
Let's tray to applay T-sne for this data before doing any data prossising and see the results.
In [6]:
#make a copy for the original dataset
df_copy=df.copy()
df_copy.drop(columns='CUST_ID',inplace=True)
In [25]:
tsne = TSNE(random_state=42,n_components=2 , perplexity=42,learning_rate=50.5)
df_copy_tsne = tsne.fit_transform(df_copy)
tsne_as_df=pd.DataFrame(df_copy_tsne)
sns.scatterplot(x=tsne_as_df[0],y=tsne_as_df[1])
Out[25]:
<Axes: xlabel='0', ylabel='1'>
not a helpfull result.
what about reducing the dimentions to 3D insted of 2D?
In [ ]:
tsne = TSNE(random_state=42,n_components=3 , perplexity=10)
df_copy_tsne = tsne.fit_transform(df_copy)
tsne_as_df=pd.DataFrame(df_copy_tsne)
# sns.pairplot(pd.DataFrame(df_copy_tsne))
In [27]:
#from mpl_toolkits.mplot3d import Axes3D
tsne_as_df=pd.DataFrame(df_copy_tsne)
fig = plt.figure(figsize=(10, 8))
ax = fig.add_subplot(111, projection='3d')
ax.scatter(tsne_as_df[0], tsne_as_df[1], tsne_as_df[2],s=5)
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
ax.view_init( elev = 15,azim=120)
plt.show()
Out[27]:
<mpl_toolkits.mplot3d.art3d.Path3DCollection at 0x112441b3250>
Out[27]:
Text(0.5, 0, 'X')
Out[27]:
Text(0.5, 0.5, 'Y')
Out[27]:
Text(0.5, 0, 'Z')
Running k-means on that to cluster our data will not be helpful.
we should do some data preprocessing first.
Define below all the issues that you had found in the previous part¶
1- one null value at CREDIT_LIMIT, and 313 null values at MINIMUM_PAYMENTS.
2- So many sparce and skueed features.
3- Droping CUST_ID Column.
4- Outlayers.
for each issue adapt this methodology¶
- start by defining the solution
- apply this solution onn the data
- test the solution to make sure that you have solved the issue
First issue
Droppig null values and unnassesary culumns
In [6]:
#solution
df.drop('CUST_ID',axis=1, inplace=True)
df.dropna(axis = 0,inplace=True)
In [14]:
#test
df.info()
<class 'pandas.core.frame.DataFrame'> Int64Index: 8636 entries, 0 to 8949 Data columns (total 17 columns): # Column Non-Null Count Dtype --- ------ -------------- ----- 0 BALANCE 8636 non-null float64 1 BALANCE_FREQUENCY 8636 non-null float64 2 PURCHASES 8636 non-null float64 3 ONEOFF_PURCHASES 8636 non-null float64 4 INSTALLMENTS_PURCHASES 8636 non-null float64 5 CASH_ADVANCE 8636 non-null float64 6 PURCHASES_FREQUENCY 8636 non-null float64 7 ONEOFF_PURCHASES_FREQUENCY 8636 non-null float64 8 PURCHASES_INSTALLMENTS_FREQUENCY 8636 non-null float64 9 CASH_ADVANCE_FREQUENCY 8636 non-null float64 10 CASH_ADVANCE_TRX 8636 non-null int64 11 PURCHASES_TRX 8636 non-null int64 12 CREDIT_LIMIT 8636 non-null float64 13 PAYMENTS 8636 non-null float64 14 MINIMUM_PAYMENTS 8636 non-null float64 15 PRC_FULL_PAYMENT 8636 non-null float64 16 TENURE 8636 non-null int64 dtypes: float64(14), int64(3) memory usage: 1.2 MB
Handling data skewness and outer layers by applying log transformation.
Trying MinMax scaler on (open limits features).
In [7]:
open_limits_features = ['BALANCE',
'PURCHASES',
'ONEOFF_PURCHASES',
'INSTALLMENTS_PURCHASES',
'CASH_ADVANCE', 'CREDIT_LIMIT',
'PAYMENTS',
'MINIMUM_PAYMENTS',
'CASH_ADVANCE_TRX',
'PURCHASES_TRX'
]
bounded_limits_features = ['BALANCE_FREQUENCY',
'PURCHASES_FREQUENCY',
'ONEOFF_PURCHASES_FREQUENCY',
'PURCHASES_INSTALLMENTS_FREQUENCY',
'CASH_ADVANCE_FREQUENCY',
'PRC_FULL_PAYMENT',
'TENURE' ]
In [12]:
df_copy_Open = df_copy[open_limits_features]
min_max = MinMaxScaler(feature_range=(0,1))
scaled_data = min_max.fit_transform(df_copy_Open)
scaled_data = pd.DataFrame(scaled_data)
scaled_data.rename(columns={
0: 'BALANCE',
1: 'PURCHASES',
2: 'ONEOFF_PURCHASES',
3: 'INSTALLMENTS_PURCHASES',
4: 'CASH_ADVANCE',
5: 'CREDIT_LIMIT',
6: 'PAYMENTS',
7: 'MINIMUM_PAYMENTS',
8: 'CASH_ADVANCE_TRX',
9: 'PURCHASES_TRX'
}, inplace=True)
scaled_data[bounded_limits_features] = df_copy[bounded_limits_features]
scaled_data.head()
Out[12]:
| BALANCE | PURCHASES | ONEOFF_PURCHASES | INSTALLMENTS_PURCHASES | CASH_ADVANCE | CREDIT_LIMIT | PAYMENTS | MINIMUM_PAYMENTS | CASH_ADVANCE_TRX | PURCHASES_TRX | BALANCE_FREQUENCY | PURCHASES_FREQUENCY | ONEOFF_PURCHASES_FREQUENCY | PURCHASES_INSTALLMENTS_FREQUENCY | CASH_ADVANCE_FREQUENCY | PRC_FULL_PAYMENT | TENURE | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 0.002148 | 0.001945 | 0.000000 | 0.004240 | 0.000000 | 0.031720 | 0.003978 | 0.001826 | 0.00000 | 0.005587 | 0.818182 | 0.166667 | 0.000000 | 0.083333 | 0.00 | 0.000000 | 12.0 |
| 1 | 0.168169 | 0.000000 | 0.000000 | 0.000000 | 0.136685 | 0.232053 | 0.080892 | 0.014034 | 0.03252 | 0.000000 | 0.909091 | 0.000000 | 0.000000 | 0.000000 | 0.25 | 0.222222 | 12.0 |
| 2 | 0.131026 | 0.015766 | 0.018968 | 0.000000 | 0.000000 | 0.248748 | 0.012263 | 0.008210 | 0.00000 | 0.033520 | 1.000000 | 1.000000 | 1.000000 | 0.000000 | 0.00 | 0.000000 | 12.0 |
| 3 | 0.042940 | 0.000326 | 0.000393 | 0.000000 | 0.000000 | 0.038397 | 0.013373 | 0.003204 | 0.00000 | 0.002793 | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
| 4 | 0.095038 | 0.027188 | 0.000000 | 0.059257 | 0.000000 | 0.058431 | 0.027602 | 0.031506 | 0.00000 | 0.022346 | 1.000000 | 0.083333 | 0.083333 | 0.000000 | 0.00 | 0.000000 | 12.0 |
In [55]:
tsne = TSNE(random_state=42,n_components=2 , perplexity=42,learning_rate=50.5)
df_copy_tsne = tsne.fit_transform(scaled_data)
tsne_as_df=pd.DataFrame(df_copy_tsne)
sns.scatterplot(x=tsne_as_df[0],y=tsne_as_df[1])
Out[55]:
<Axes: xlabel='0', ylabel='1'>
Still not good, let's try a different transformation method.
the log function is equipped to deal with large numbers. so we will applay it to the coulomns with large and small numbers (open limits features).
In [9]:
#solution
log_scaled_data = np.log1p(df[open_limits_features])
log_scaled_data[bounded_limits_features] = df[bounded_limits_features]
log_scaled_data.head()
Out[9]:
| BALANCE | PURCHASES | ONEOFF_PURCHASES | INSTALLMENTS_PURCHASES | CASH_ADVANCE | CREDIT_LIMIT | PAYMENTS | MINIMUM_PAYMENTS | CASH_ADVANCE_TRX | PURCHASES_TRX | BALANCE_FREQUENCY | PURCHASES_FREQUENCY | ONEOFF_PURCHASES_FREQUENCY | PURCHASES_INSTALLMENTS_FREQUENCY | CASH_ADVANCE_FREQUENCY | PRC_FULL_PAYMENT | TENURE | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 3.735304 | 4.568506 | 0.000000 | 4.568506 | 0.000000 | 6.908755 | 5.312231 | 4.945277 | 0.000000 | 1.098612 | 0.818182 | 0.166667 | 0.000000 | 0.083333 | 0.00 | 0.000000 | 12 |
| 1 | 8.071989 | 0.000000 | 0.000000 | 0.000000 | 8.770896 | 8.853808 | 8.319725 | 6.978531 | 1.609438 | 0.000000 | 0.909091 | 0.000000 | 0.000000 | 0.000000 | 0.25 | 0.222222 | 12 |
| 2 | 7.822504 | 6.651791 | 6.651791 | 0.000000 | 0.000000 | 8.922792 | 6.434654 | 6.442994 | 0.000000 | 2.564949 | 1.000000 | 1.000000 | 1.000000 | 0.000000 | 0.00 | 0.000000 | 12 |
| 4 | 6.707735 | 2.833213 | 2.833213 | 0.000000 | 0.000000 | 7.090910 | 6.521114 | 5.504483 | 0.000000 | 0.693147 | 1.000000 | 0.083333 | 0.083333 | 0.000000 | 0.00 | 0.000000 | 12 |
| 5 | 7.501540 | 7.196147 | 0.000000 | 7.196147 | 0.000000 | 7.496097 | 7.244983 | 7.786654 | 0.000000 | 2.197225 | 1.000000 | 0.666667 | 0.000000 | 0.583333 | 0.00 | 0.000000 | 12 |
In [22]:
#test
log_scaled_data.describe().T
Out[22]:
| count | mean | std | min | 25% | 50% | 75% | max | |
|---|---|---|---|---|---|---|---|---|
| BALANCE | 8636.0 | 6.265737 | 1.895982 | 0.000000 | 5.004584 | 6.822040 | 7.652639 | 9.854515 |
| PURCHASES | 8636.0 | 4.928905 | 2.922819 | 0.000000 | 3.792507 | 5.930666 | 7.044888 | 10.800403 |
| ONEOFF_PURCHASES | 8636.0 | 3.239500 | 3.252619 | 0.000000 | 0.000000 | 3.828533 | 6.397096 | 10.615512 |
| INSTALLMENTS_PURCHASES | 8636.0 | 3.387883 | 3.091009 | 0.000000 | 0.000000 | 4.562106 | 6.184453 | 10.021315 |
| CASH_ADVANCE | 8636.0 | 3.349135 | 3.571114 | 0.000000 | 0.000000 | 0.000000 | 7.032964 | 10.760839 |
| CREDIT_LIMIT | 8636.0 | 8.099572 | 0.822341 | 3.931826 | 7.378384 | 8.006701 | 8.779711 | 10.308986 |
| PAYMENTS | 8636.0 | 6.814890 | 1.159994 | 0.048326 | 6.039205 | 6.799809 | 7.576683 | 10.834125 |
| MINIMUM_PAYMENTS | 8636.0 | 5.922564 | 1.190068 | 0.018982 | 5.136760 | 5.747647 | 6.717196 | 11.243832 |
| CASH_ADVANCE_TRX | 8636.0 | 0.829327 | 1.015146 | 0.000000 | 0.000000 | 0.000000 | 1.609438 | 4.820282 |
| PURCHASES_TRX | 8636.0 | 1.916439 | 1.378707 | 0.000000 | 0.693147 | 2.079442 | 2.944439 | 5.883322 |
| BALANCE_FREQUENCY | 8636.0 | 0.895035 | 0.207697 | 0.000000 | 0.909091 | 1.000000 | 1.000000 | 1.000000 |
| PURCHASES_FREQUENCY | 8636.0 | 0.496000 | 0.401273 | 0.000000 | 0.083333 | 0.500000 | 0.916667 | 1.000000 |
| ONEOFF_PURCHASES_FREQUENCY | 8636.0 | 0.205909 | 0.300054 | 0.000000 | 0.000000 | 0.083333 | 0.333333 | 1.000000 |
| PURCHASES_INSTALLMENTS_FREQUENCY | 8636.0 | 0.368820 | 0.398093 | 0.000000 | 0.000000 | 0.166667 | 0.750000 | 1.000000 |
| CASH_ADVANCE_FREQUENCY | 8636.0 | 0.137604 | 0.201791 | 0.000000 | 0.000000 | 0.000000 | 0.250000 | 1.500000 |
| PRC_FULL_PAYMENT | 8636.0 | 0.159304 | 0.296271 | 0.000000 | 0.000000 | 0.000000 | 0.166667 | 1.000000 |
| TENURE | 8636.0 | 11.534391 | 1.310984 | 6.000000 | 12.000000 | 12.000000 | 12.000000 | 12.000000 |
Let's tray to applay T-sne to the log transformed data.
In [59]:
tsne = TSNE(random_state=42,n_components=2 , perplexity=42,learning_rate=50.5)
df_copy_tsne = tsne.fit_transform(log_scaled_data)
tsne_as_df=pd.DataFrame(df_copy_tsne)
sns.scatterplot(x=tsne_as_df[0],y=tsne_as_df[1])
Out[59]:
<Axes: xlabel='0', ylabel='1'>
Amazing !!
by looking at the picture I think T-sne suggests a 7 groupes.
we can also use elbow curve to make shure ( latter ).
PCA Vs. Kernal PCA¶
In [54]:
pca = PCA(n_components=.95) # save 95% of the fuetures
kernel_pca = KernelPCA(n_components = 15,
kernel="rbf", gamma=10, fit_inverse_transform=True, alpha=0.1
)
Data_pca = pca.fit_transform(log_scaled_data)
Data_kernel_pca = kernel_pca.fit_transform(log_scaled_data)
In [55]:
Data_kernel_pca.shape
Data_pca.shape
Data_pca = pd.DataFrame(Data_pca)
Data_kernel_pca = pd.DataFrame(Data_kernel_pca)
Out[55]:
(8636, 15)
Out[55]:
(8636, 6)
Applaying T-sne on linear PCA.
In [89]:
tsne = TSNE(random_state=42,n_components=2 , perplexity=42,learning_rate=50.5)
df_copy_tsne = tsne.fit_transform(Data_pca)
tsne_as_df_PCA=pd.DataFrame(df_copy_tsne)
sns.scatterplot(x=tsne_as_df_PCA[0],y=tsne_as_df_PCA[1])
Out[89]:
<Axes: xlabel='0', ylabel='1'>
It looks like PCA performed well in this data.
and visualy it seems that T-sne suggests 7 clusters.
Applaying T-sne on kernel PCA.
In [56]:
tsne = TSNE(random_state=42,n_components=2 , perplexity=42,learning_rate=50.5)
df_copy_tsne = tsne.fit_transform(Data_kernel_pca)
tsne_as_df=pd.DataFrame(df_copy_tsne)
sns.scatterplot(x=tsne_as_df[0],y=tsne_as_df[1])
Out[56]:
<Axes: xlabel='0', ylabel='1'>
It looks like the kernel PCA has some sort of hummer. 😅
Let's tray the default parameters with ‘sigmoid’.
In [36]:
kernel_pca = KernelPCA(n_components = 16,kernel="sigmoid")
Data_kernel_pca = kernel_pca.fit_transform(log_scaled_data)
In [37]:
tsne = TSNE(random_state=42,n_components=2 , perplexity=42,learning_rate=50.5)
df_copy_tsne = tsne.fit_transform(Data_kernel_pca)
tsne_as_df=pd.DataFrame(df_copy_tsne)
sns.scatterplot(x=tsne_as_df[0],y=tsne_as_df[1])
Out[37]:
<Axes: xlabel='0', ylabel='1'>
stell not good, let's see poly
In [88]:
kernel_pca = KernelPCA(n_components = 16,kernel="poly")
Data_kernel_pca = kernel_pca.fit_transform(log_scaled_data)
tsne = TSNE(random_state=42,n_components=2 , perplexity=42,learning_rate=50.5)
df_copy_tsne = tsne.fit_transform(Data_kernel_pca)
tsne_as_df_Kernel_PCA=pd.DataFrame(df_copy_tsne)
sns.scatterplot(x=tsne_as_df_Kernel_PCA[0],y=tsne_as_df_Kernel_PCA[1])
Out[88]:
<Axes: xlabel='0', ylabel='1'>
Amazing!!
DBSCAN¶
In [131]:
dbscan = DBSCAN(eps=2.6, min_samples=5)
dbscan_clusters = dbscan.fit(log_scaled_data)
In [132]:
pd.DataFrame(dbscan_clusters.labels_).value_counts()
Out[132]:
0 4405 1 1959 2 1415 3 749 -1 108 dtype: int64
In [136]:
names = {-1: 'No class',
0: 'Clsss A',
1: 'Class B',
2: 'Class C',
3: 'Class D',
}
# Replace cluster labels with names
cluster_labels = [names[label] for label in dbscan_clusters.labels_]
# Scatter plot
sns.scatterplot(x=tsne_as_df[0], y=tsne_as_df[1], hue=cluster_labels)
plt.legend(loc='upper left', bbox_to_anchor=(1, 0.4))
plt.show()
Out[136]:
<Axes: xlabel='0', ylabel='1'>
Out[136]:
<matplotlib.legend.Legend at 0x223b7596690>
What is the feature scaling technique that would use and why?
return to this section again and try another technique and see how that will impact your result
for more details on different methods for scaling check these links
Answer here:
In [139]:
from scipy.cluster.hierarchy import dendrogram, ward, single
link_mat = ward(log_scaled_data)
dendrogram(link_mat)
plt.show()
Out[139]:
{'icoord': [[15.0, 15.0, 25.0, 25.0],
[5.0, 5.0, 20.0, 20.0],
[45.0, 45.0, 55.0, 55.0],
[35.0, 35.0, 50.0, 50.0],
[75.0, 75.0, 85.0, 85.0],
[65.0, 65.0, 80.0, 80.0],
[95.0, 95.0, 105.0, 105.0],
[125.0, 125.0, 135.0, 135.0],
[115.0, 115.0, 130.0, 130.0],
[100.0, 100.0, 122.5, 122.5],
[72.5, 72.5, 111.25, 111.25],
[42.5, 42.5, 91.875, 91.875],
[12.5, 12.5, 67.1875, 67.1875],
[155.0, 155.0, 165.0, 165.0],
[175.0, 175.0, 185.0, 185.0],
[160.0, 160.0, 180.0, 180.0],
[145.0, 145.0, 170.0, 170.0],
[225.0, 225.0, 235.0, 235.0],
[215.0, 215.0, 230.0, 230.0],
[205.0, 205.0, 222.5, 222.5],
[195.0, 195.0, 213.75, 213.75],
[157.5, 157.5, 204.375, 204.375],
[245.0, 245.0, 255.0, 255.0],
[265.0, 265.0, 275.0, 275.0],
[250.0, 250.0, 270.0, 270.0],
[295.0, 295.0, 305.0, 305.0],
[285.0, 285.0, 300.0, 300.0],
[325.0, 325.0, 335.0, 335.0],
[355.0, 355.0, 365.0, 365.0],
[345.0, 345.0, 360.0, 360.0],
[330.0, 330.0, 352.5, 352.5],
[315.0, 315.0, 341.25, 341.25],
[292.5, 292.5, 328.125, 328.125],
[260.0, 260.0, 310.3125, 310.3125],
[180.9375, 180.9375, 285.15625, 285.15625],
[39.84375, 39.84375, 233.046875, 233.046875],
[395.0, 395.0, 405.0, 405.0],
[385.0, 385.0, 400.0, 400.0],
[415.0, 415.0, 425.0, 425.0],
[392.5, 392.5, 420.0, 420.0],
[375.0, 375.0, 406.25, 406.25],
[435.0, 435.0, 445.0, 445.0],
[455.0, 455.0, 465.0, 465.0],
[440.0, 440.0, 460.0, 460.0],
[495.0, 495.0, 505.0, 505.0],
[525.0, 525.0, 535.0, 535.0],
[515.0, 515.0, 530.0, 530.0],
[500.0, 500.0, 522.5, 522.5],
[485.0, 485.0, 511.25, 511.25],
[475.0, 475.0, 498.125, 498.125],
[450.0, 450.0, 486.5625, 486.5625],
[390.625, 390.625, 468.28125, 468.28125],
[555.0, 555.0, 565.0, 565.0],
[545.0, 545.0, 560.0, 560.0],
[585.0, 585.0, 595.0, 595.0],
[575.0, 575.0, 590.0, 590.0],
[552.5, 552.5, 582.5, 582.5],
[625.0, 625.0, 635.0, 635.0],
[615.0, 615.0, 630.0, 630.0],
[605.0, 605.0, 622.5, 622.5],
[655.0, 655.0, 665.0, 665.0],
[675.0, 675.0, 685.0, 685.0],
[660.0, 660.0, 680.0, 680.0],
[645.0, 645.0, 670.0, 670.0],
[613.75, 613.75, 657.5, 657.5],
[567.5, 567.5, 635.625, 635.625],
[429.453125, 429.453125, 601.5625, 601.5625],
[705.0, 705.0, 715.0, 715.0],
[695.0, 695.0, 710.0, 710.0],
[735.0, 735.0, 745.0, 745.0],
[725.0, 725.0, 740.0, 740.0],
[702.5, 702.5, 732.5, 732.5],
[755.0, 755.0, 765.0, 765.0],
[785.0, 785.0, 795.0, 795.0],
[775.0, 775.0, 790.0, 790.0],
[760.0, 760.0, 782.5, 782.5],
[835.0, 835.0, 845.0, 845.0],
[825.0, 825.0, 840.0, 840.0],
[815.0, 815.0, 832.5, 832.5],
[805.0, 805.0, 823.75, 823.75],
[771.25, 771.25, 814.375, 814.375],
[717.5, 717.5, 792.8125, 792.8125],
[855.0, 855.0, 865.0, 865.0],
[875.0, 875.0, 885.0, 885.0],
[895.0, 895.0, 905.0, 905.0],
[880.0, 880.0, 900.0, 900.0],
[860.0, 860.0, 890.0, 890.0],
[945.0, 945.0, 955.0, 955.0],
[935.0, 935.0, 950.0, 950.0],
[925.0, 925.0, 942.5, 942.5],
[915.0, 915.0, 933.75, 933.75],
[975.0, 975.0, 985.0, 985.0],
[965.0, 965.0, 980.0, 980.0],
[1005.0, 1005.0, 1015.0, 1015.0],
[995.0, 995.0, 1010.0, 1010.0],
[1025.0, 1025.0, 1035.0, 1035.0],
[1002.5, 1002.5, 1030.0, 1030.0],
[972.5, 972.5, 1016.25, 1016.25],
[924.375, 924.375, 994.375, 994.375],
[875.0, 875.0, 959.375, 959.375],
[1045.0, 1045.0, 1055.0, 1055.0],
[1065.0, 1065.0, 1075.0, 1075.0],
[1085.0, 1085.0, 1095.0, 1095.0],
[1070.0, 1070.0, 1090.0, 1090.0],
[1050.0, 1050.0, 1080.0, 1080.0],
[1105.0, 1105.0, 1115.0, 1115.0],
[1125.0, 1125.0, 1135.0, 1135.0],
[1145.0, 1145.0, 1155.0, 1155.0],
[1130.0, 1130.0, 1150.0, 1150.0],
[1165.0, 1165.0, 1175.0, 1175.0],
[1185.0, 1185.0, 1195.0, 1195.0],
[1170.0, 1170.0, 1190.0, 1190.0],
[1140.0, 1140.0, 1180.0, 1180.0],
[1110.0, 1110.0, 1160.0, 1160.0],
[1065.0, 1065.0, 1135.0, 1135.0],
[917.1875, 917.1875, 1100.0, 1100.0],
[755.15625, 755.15625, 1008.59375, 1008.59375],
[515.5078125, 515.5078125, 881.875, 881.875],
[1205.0, 1205.0, 1215.0, 1215.0],
[1235.0, 1235.0, 1245.0, 1245.0],
[1225.0, 1225.0, 1240.0, 1240.0],
[1210.0, 1210.0, 1232.5, 1232.5],
[1255.0, 1255.0, 1265.0, 1265.0],
[1275.0, 1275.0, 1285.0, 1285.0],
[1315.0, 1315.0, 1325.0, 1325.0],
[1305.0, 1305.0, 1320.0, 1320.0],
[1295.0, 1295.0, 1312.5, 1312.5],
[1280.0, 1280.0, 1303.75, 1303.75],
[1260.0, 1260.0, 1291.875, 1291.875],
[1345.0, 1345.0, 1355.0, 1355.0],
[1365.0, 1365.0, 1375.0, 1375.0],
[1350.0, 1350.0, 1370.0, 1370.0],
[1335.0, 1335.0, 1360.0, 1360.0],
[1275.9375, 1275.9375, 1347.5, 1347.5],
[1221.25, 1221.25, 1311.71875, 1311.71875],
[1385.0, 1385.0, 1395.0, 1395.0],
[1415.0, 1415.0, 1425.0, 1425.0],
[1405.0, 1405.0, 1420.0, 1420.0],
[1390.0, 1390.0, 1412.5, 1412.5],
[1445.0, 1445.0, 1455.0, 1455.0],
[1465.0, 1465.0, 1475.0, 1475.0],
[1450.0, 1450.0, 1470.0, 1470.0],
[1435.0, 1435.0, 1460.0, 1460.0],
[1485.0, 1485.0, 1495.0, 1495.0],
[1505.0, 1505.0, 1515.0, 1515.0],
[1545.0, 1545.0, 1555.0, 1555.0],
[1535.0, 1535.0, 1550.0, 1550.0],
[1525.0, 1525.0, 1542.5, 1542.5],
[1510.0, 1510.0, 1533.75, 1533.75],
[1490.0, 1490.0, 1521.875, 1521.875],
[1447.5, 1447.5, 1505.9375, 1505.9375],
[1401.25, 1401.25, 1476.71875, 1476.71875],
[1565.0, 1565.0, 1575.0, 1575.0],
[1585.0, 1585.0, 1595.0, 1595.0],
[1615.0, 1615.0, 1625.0, 1625.0],
[1605.0, 1605.0, 1620.0, 1620.0],
[1635.0, 1635.0, 1645.0, 1645.0],
[1612.5, 1612.5, 1640.0, 1640.0],
[1590.0, 1590.0, 1626.25, 1626.25],
[1570.0, 1570.0, 1608.125, 1608.125],
[1655.0, 1655.0, 1665.0, 1665.0],
[1675.0, 1675.0, 1685.0, 1685.0],
[1695.0, 1695.0, 1705.0, 1705.0],
[1715.0, 1715.0, 1725.0, 1725.0],
[1735.0, 1735.0, 1745.0, 1745.0],
[1720.0, 1720.0, 1740.0, 1740.0],
[1700.0, 1700.0, 1730.0, 1730.0],
[1680.0, 1680.0, 1715.0, 1715.0],
[1660.0, 1660.0, 1697.5, 1697.5],
[1589.0625, 1589.0625, 1678.75, 1678.75],
[1438.984375, 1438.984375, 1633.90625, 1633.90625],
[1266.484375, 1266.484375, 1536.4453125, 1536.4453125],
[698.69140625, 698.69140625, 1401.46484375, 1401.46484375],
[136.4453125, 136.4453125, 1050.078125, 1050.078125],
[1765.0, 1765.0, 1775.0, 1775.0],
[1755.0, 1755.0, 1770.0, 1770.0],
[1795.0, 1795.0, 1805.0, 1805.0],
[1785.0, 1785.0, 1800.0, 1800.0],
[1762.5, 1762.5, 1792.5, 1792.5],
[1825.0, 1825.0, 1835.0, 1835.0],
[1815.0, 1815.0, 1830.0, 1830.0],
[1855.0, 1855.0, 1865.0, 1865.0],
[1845.0, 1845.0, 1860.0, 1860.0],
[1875.0, 1875.0, 1885.0, 1885.0],
[1852.5, 1852.5, 1880.0, 1880.0],
[1822.5, 1822.5, 1866.25, 1866.25],
[1777.5, 1777.5, 1844.375, 1844.375],
[1905.0, 1905.0, 1915.0, 1915.0],
[1895.0, 1895.0, 1910.0, 1910.0],
[1925.0, 1925.0, 1935.0, 1935.0],
[1955.0, 1955.0, 1965.0, 1965.0],
[1945.0, 1945.0, 1960.0, 1960.0],
[1930.0, 1930.0, 1952.5, 1952.5],
[1902.5, 1902.5, 1941.25, 1941.25],
[1975.0, 1975.0, 1985.0, 1985.0],
[2015.0, 2015.0, 2025.0, 2025.0],
[2005.0, 2005.0, 2020.0, 2020.0],
[1995.0, 1995.0, 2012.5, 2012.5],
[1980.0, 1980.0, 2003.75, 2003.75],
[2035.0, 2035.0, 2045.0, 2045.0],
[2065.0, 2065.0, 2075.0, 2075.0],
[2055.0, 2055.0, 2070.0, 2070.0],
[2040.0, 2040.0, 2062.5, 2062.5],
[2085.0, 2085.0, 2095.0, 2095.0],
[2105.0, 2105.0, 2115.0, 2115.0],
[2090.0, 2090.0, 2110.0, 2110.0],
[2051.25, 2051.25, 2100.0, 2100.0],
[1991.875, 1991.875, 2075.625, 2075.625],
[1921.875, 1921.875, 2033.75, 2033.75],
[1810.9375, 1810.9375, 1977.8125, 1977.8125],
[2125.0, 2125.0, 2135.0, 2135.0],
[2155.0, 2155.0, 2165.0, 2165.0],
[2145.0, 2145.0, 2160.0, 2160.0],
[2195.0, 2195.0, 2205.0, 2205.0],
[2185.0, 2185.0, 2200.0, 2200.0],
[2175.0, 2175.0, 2192.5, 2192.5],
[2152.5, 2152.5, 2183.75, 2183.75],
[2130.0, 2130.0, 2168.125, 2168.125],
[2245.0, 2245.0, 2255.0, 2255.0],
[2235.0, 2235.0, 2250.0, 2250.0],
[2225.0, 2225.0, 2242.5, 2242.5],
[2295.0, 2295.0, 2305.0, 2305.0],
[2285.0, 2285.0, 2300.0, 2300.0],
[2275.0, 2275.0, 2292.5, 2292.5],
[2265.0, 2265.0, 2283.75, 2283.75],
[2233.75, 2233.75, 2274.375, 2274.375],
[2215.0, 2215.0, 2254.0625, 2254.0625],
[2149.0625, 2149.0625, 2234.53125, 2234.53125],
[1894.375, 1894.375, 2191.796875, 2191.796875],
[2335.0, 2335.0, 2345.0, 2345.0],
[2325.0, 2325.0, 2340.0, 2340.0],
[2315.0, 2315.0, 2332.5, 2332.5],
[2355.0, 2355.0, 2365.0, 2365.0],
[2385.0, 2385.0, 2395.0, 2395.0],
[2375.0, 2375.0, 2390.0, 2390.0],
[2360.0, 2360.0, 2382.5, 2382.5],
[2323.75, 2323.75, 2371.25, 2371.25],
[2415.0, 2415.0, 2425.0, 2425.0],
[2405.0, 2405.0, 2420.0, 2420.0],
[2435.0, 2435.0, 2445.0, 2445.0],
[2455.0, 2455.0, 2465.0, 2465.0],
[2440.0, 2440.0, 2460.0, 2460.0],
[2475.0, 2475.0, 2485.0, 2485.0],
[2495.0, 2495.0, 2505.0, 2505.0],
[2480.0, 2480.0, 2500.0, 2500.0],
[2450.0, 2450.0, 2490.0, 2490.0],
[2412.5, 2412.5, 2470.0, 2470.0],
[2347.5, 2347.5, 2441.25, 2441.25],
[2525.0, 2525.0, 2535.0, 2535.0],
[2555.0, 2555.0, 2565.0, 2565.0],
[2545.0, 2545.0, 2560.0, 2560.0],
[2530.0, 2530.0, 2552.5, 2552.5],
[2575.0, 2575.0, 2585.0, 2585.0],
[2615.0, 2615.0, 2625.0, 2625.0],
[2605.0, 2605.0, 2620.0, 2620.0],
[2595.0, 2595.0, 2612.5, 2612.5],
[2580.0, 2580.0, 2603.75, 2603.75],
[2541.25, 2541.25, 2591.875, 2591.875],
[2645.0, 2645.0, 2655.0, 2655.0],
[2635.0, 2635.0, 2650.0, 2650.0],
[2665.0, 2665.0, 2675.0, 2675.0],
[2685.0, 2685.0, 2695.0, 2695.0],
[2670.0, 2670.0, 2690.0, 2690.0],
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hierarchy clasters also shows 7 clasters.
1- Use the k means class that you implemented in the previous task to cluster this data 2- Use http://scikit-learn.org/stable/modules/generated/sklearn.cluster.KMeans.html and see if the difference in the result 3- Use elbow method to determine the K (plot the result using two plot one for distorion and another for inertia) 4- (Optionally) make a method that pick the best number of clusters for you 5- Using different techniques for scaling and comment on the result
In [10]:
inertias = []
k_range = range(3, 16)
for k in k_range:
kmeans = KMeans(n_clusters=k, random_state=42)
kmeans.fit(log_scaled_data)
inertias.append(kmeans.inertia_)
Out[10]:
KMeans(n_clusters=3, random_state=42)In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
KMeans(n_clusters=3, random_state=42)
Out[10]:
KMeans(n_clusters=4, random_state=42)In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
KMeans(n_clusters=4, random_state=42)
Out[10]:
KMeans(n_clusters=5, random_state=42)In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
KMeans(n_clusters=5, random_state=42)
Out[10]:
KMeans(n_clusters=6, random_state=42)In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
KMeans(n_clusters=6, random_state=42)
Out[10]:
KMeans(n_clusters=7, random_state=42)In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
KMeans(n_clusters=7, random_state=42)
Out[10]:
KMeans(random_state=42)In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
KMeans(random_state=42)
Out[10]:
KMeans(n_clusters=9, random_state=42)In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
KMeans(n_clusters=9, random_state=42)
Out[10]:
KMeans(n_clusters=10, random_state=42)In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
KMeans(n_clusters=10, random_state=42)
Out[10]:
KMeans(n_clusters=11, random_state=42)In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
KMeans(n_clusters=11, random_state=42)
Out[10]:
KMeans(n_clusters=12, random_state=42)In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
KMeans(n_clusters=12, random_state=42)
Out[10]:
KMeans(n_clusters=13, random_state=42)In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
KMeans(n_clusters=13, random_state=42)
Out[10]:
KMeans(n_clusters=14, random_state=42)In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
KMeans(n_clusters=14, random_state=42)
Out[10]:
KMeans(n_clusters=15, random_state=42)In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
KMeans(n_clusters=15, random_state=42)
In [83]:
# Plot Inertia
plt.plot(k_range, inertias, marker='o')
plt.xlabel('Number of Clusters (K)')
plt.ylabel('Inertia')
plt.title('Elbow Method for Optimal K (Inertia)')
plt.show()
Out[83]:
[<matplotlib.lines.Line2D at 0x223b3e2c6d0>]
Out[83]:
Text(0.5, 0, 'Number of Clusters (K)')
Out[83]:
Text(0, 0.5, 'Inertia')
Out[83]:
Text(0.5, 1.0, 'Elbow Method for Optimal K (Inertia)')
according to elbow plot we chose 7 clusters.
In [11]:
kmeans = KMeans(n_clusters=7, random_state=0).fit(log_scaled_data)
!!! Driving business insights part was moved to the end of the notebook !!!¶
In [85]:
names = {0: 'Low cost purchases',
1: 'no installment purchases,low Purchase frequency',
2: 'no chas advance,low balance, high oneoff purchases',
3: 'No purchases,low cost cash advance',
4: 'no oneoff purchases or cash advance',
5:'clients make installment(high rate),',
6:'clients with Low balance,no installment,no cash advance'}
# Replace cluster labels with names
cluster_labels = [names[label] for label in kmeans.labels_]
# Scatter plot
sns.scatterplot(x=tsne_as_df[0], y=tsne_as_df[1], hue=cluster_labels)
plt.legend(loc='upper left', bbox_to_anchor=(1, 0.4))
plt.show()
Out[85]:
<Axes: xlabel='0', ylabel='1'>
Out[85]:
<matplotlib.legend.Legend at 0x223b242ac50>
In [91]:
# Scatter plot for PCA.
sns.scatterplot(x=tsne_as_df_PCA[0], y=tsne_as_df_PCA[1], hue=cluster_labels)
plt.legend(loc='upper left', bbox_to_anchor=(1, 0.4))
plt.show()
Out[91]:
<Axes: xlabel='0', ylabel='1'>
Out[91]:
<matplotlib.legend.Legend at 0x223b44a4850>
In [92]:
# Scatter plot for kernal PCA.
sns.scatterplot(x=tsne_as_df_Kernel_PCA[0], y=tsne_as_df_Kernel_PCA[1], hue=cluster_labels)
plt.legend(loc='upper left', bbox_to_anchor=(1, 0.4))
plt.show()
Out[92]:
<Axes: xlabel='0', ylabel='1'>
Out[92]:
<matplotlib.legend.Legend at 0x223b4a52c50>
3D T-sne
In [94]:
tsne = TSNE(random_state=42,n_components=3 , perplexity=10)
df_copy_tsne_3D = tsne.fit_transform(log_scaled_data)
df_copy_tsne_3D=pd.DataFrame(df_copy_tsne_3D)
In [97]:
fig = plt.figure(figsize=(10, 8))
ax = fig.add_subplot(111, projection='3d')
# Assuming kmeans.labels_ contains the cluster labels for each point
ax.scatter(df_copy_tsne_3D[0], df_copy_tsne_3D[1], df_copy_tsne_3D[2], c=kmeans.labels_, s=5, cmap='viridis')
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
ax.view_init(elev=15, azim=120)
# Add color bar
cbar = plt.colorbar(ax.scatter([], [], [], c=[], cmap='viridis'), ax=ax)
cbar.set_label('Cluster')
plt.show()
Out[97]:
<mpl_toolkits.mplot3d.art3d.Path3DCollection at 0x223b51178d0>
Out[97]:
Text(0.5, 0, 'X')
Out[97]:
Text(0.5, 0.5, 'Y')
Out[97]:
Text(0.5, 0, 'Z')
In [24]:
fig = plt.figure(figsize=(10, 8))
ax = fig.add_subplot(111, projection='3d')
# Assuming kmeans.labels_ contains the cluster labels for each point
ax.scatter(tsne_as_df[0], tsne_as_df[1], tsne_as_df[2], c=kmeans.labels_, s=5, cmap='viridis')
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
ax.view_init(elev=15, azim=120)
# Add color bar
cbar = plt.colorbar(ax.scatter([], [], [], c=[], cmap='viridis'), ax=ax)
cbar.set_label('Cluster')
plt.show()
Out[24]:
<mpl_toolkits.mplot3d.art3d.Path3DCollection at 0x1b636e421d0>
Out[24]:
Text(0.5, 0, 'X')
Out[24]:
Text(0.5, 0.5, 'Y')
Out[24]:
Text(0.5, 0, 'Z')
Before we start the training process we need to specify 3 paramters:
1- Linkage criteria : The linkage criterion determines the distance between two clusters
- Complete-Linkage Clustering
- Single-Linkage Clustering
- Average-Linkage Clustering
- Centroid Linkage Clustering
2- Distance function:
- Euclidean Distance
- Manhattan Distance
- Mahalanobis distance
3- Number of clusters
Number of clusters¶
Use Dendograms to specify the optimum number of clusters
- Compare how changing linkage criteria or distance function would affect the optimum number of clusters
- you can use silhouette_score or any other evalution method to help you determine the optimum number of clusters
https://scikit-learn.org/stable/modules/generated/sklearn.metrics.silhouette_score.html
In [ ]:
import scipy.cluster.hierarchy as shc
plt.figure(figsize=(10, 7))
plt.title("Counters Dendograms")
dend = shc.dendrogram(shc.linkage(y=... , method=...,metric=...),orientation='right') #fill y with your dataframe
#and method with linkage criteria
#and metric with distance function
In [ ]:
#training
from sklearn.cluster import AgglomerativeClustering
In [ ]:
- Try to use PCA to reduce the number of features and compare how this will affect the clustring process
- Try to run your code again but with different tranformation technique
- Implement gap statistics method and use it as evaluation metric and compare the result with what you did before https://www.datanovia.com/en/lessons/determining-the-optimal-number-of-clusters-3-must-know-methods/#gap-statistic-method
Driving busness mening¶
In [ ]:
log_scaled_data_copy = log_scaled_data.copy()
log_scaled_data_copy["labols"] = pd.DataFrame(kmeans.labels_)
log_scaled_data_copy.dropna(axis = 0,inplace=True)
In [ ]:
unique_labels = log_scaled_data_copy['labols'].unique()
# Create a dictionary to store DataFrames for each group
group_dataframes = {}
# Iterate over unique labels and create a DataFrame for each group
for label in unique_labels:
group_dataframes[label] = log_scaled_data_copy[log_scaled_data_copy['labols'] == label].copy()
In [110]:
def Bar_subplots(dfs, Column_name, bins,ii):
"""Plot a meaningful bar plot.
Args:
df (Pandas Dataframe): DataFrame with all the records.
Column_name (string): the name of the column we want to plot.
bins (list): Dividing our bar plot according to those bins.
"""
fig, axes = plt.subplots(1, 2, figsize=(18, 7)) # Create subplots for each class
for i in range(2):
df = dfs[i]
freq, bins, p = axes[i].hist(df[Column_name], bins=bins, rwidth=0.9)
# x coordinate for labels
bin_centers = np.diff(bins) * 0.5 + bins[:-1]
n = 0
for fr, x, patch in zip(freq, bin_centers, p):
height = int(freq[n])
axes[i].annotate("{}%".format(round(height * 100 / df.shape[0], 2)),
xy=(x, height),
xytext=(0, 0.2),
textcoords="offset points",
ha='center', va='bottom'
)
n = n + 1
axes[i].grid()
axes[i].set_xticks(bins)
axes[i].set_title("CLASS " + str(i+ii))
axes[i].set_xlabel(Column_name)
plt.tight_layout()
plt.show()
In [112]:
for i in log_scaled_data_copy.columns:
Bar_subplots([group_dataframes[0],group_dataframes[1]], i, [0, 1, 2, 4, 5, 9, 12],0)
In [113]:
for i in log_scaled_data_copy.columns:
Bar_subplots([group_dataframes[2],group_dataframes[3]], i, [0, 1, 2, 4, 5, 9, 12],2)
In [114]:
for i in log_scaled_data_copy.columns:
Bar_subplots([group_dataframes[4],group_dataframes[5]], i, [0, 1, 2, 4, 5, 9, 12],4)
In [115]:
for i in log_scaled_data_copy.columns:
Bar_subplots([group_dataframes[6],group_dataframes[1]], i, [0, 1, 2, 4, 5, 9, 12],6)
